Let \(\mathbb {F}_{2^n}\)  be an extension of the finite field \(\mathbb {F}_2\) . Many codes defined over \(\mathbb {F}_2\)  are subfield subcodes of another code defined over the extension \(\mathbb {F}_{2^n}\) . For instance, Alternant codes are subfield subcodes of Generalized Reed-Solomon codes and
classical Goppa codes are a special case of Alternant codes [1]}.
